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Nonlinear amplification of adhesion forces in interleaved books

  • Regular Article - Soft Matter
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Abstract

It is nearly impossible to separate two interleaved phonebooks by pulling their spines. The very slight force exerted by the outer sheets of the assembly is amplified as the exponential of the square of the number of sheets, meaning that even a small number of sheets can create a highly resistant system. We present a systematic and detailed study of the influences of the normal external force and the geometrical parameters of the booklets on the assembly strength. We conclude that the paper-paper adhesion force between the two outer sheets, on the order of a few \(\hbox {mN}\),  is the one amplified by the interleaved-book system. The two-phonebook experiment—which has attracted the attention of students and the non-scientific public all around the world as an outstanding demonstration of the strength of friction—appears to also be a spectacular macroscopic manifestation of the microscopic coupling of friction and adhesion.

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Acknowledgements

It is our great pleasure to thank K. Dalnoki-Veress for continuous discussions about this problem. We also thank C. Aujoux for unpublished preliminary results, and Mason Porter for suggesting the name “Hercules number” via the Improbable Research blog. We thank D. Labonte for his careful review of our paper. We benefited from the financial support of the ANR (ANR-17-CE08-0008).

Author information

Authors and Affiliations

  1. Laboratoire de physique des solides, CNRS, Université Paris-Saclay, Orsay, France

    Raphaelle Taub, Christophe Poulard & Frédéric Restagno

  2. Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33405, Talence, France

    Thomas Salez

  3. Global Station for Soft Matter, Global Institution for Collaborative Research and Education, Hokkaido University, Sapporo, Hokkaido, 060-0808, Japan

    Thomas Salez

  4. Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua, Chile

    Hector Alarcòn

  5. UMR CNRS 7083 Gulliver, ESPCI Paris, PSL Research University, Paris, France

    Élie Raphaël

Authors
  1. Raphaelle Taub
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  2. Thomas Salez
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  3. Hector Alarcòn
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  4. Élie Raphaël
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  5. Christophe Poulard
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  6. Frédéric Restagno
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Contributions

R.T. did the experiments. All authors interpreted the results and developed the models. R.T., F.R. and C.P. wrote the manuscript and all the authors read and corrected the manuscript.

Corresponding author

Correspondence to Christophe Poulard.

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Taub, R., Salez, T., Alarcòn, H. et al. Nonlinear amplification of adhesion forces in interleaved books. Eur. Phys. J. E 44, 71 (2021). https://doi.org/10.1140/epje/s10189-021-00068-z

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